{"paper":{"title":"Dynamics near Couette flow for the $\\beta$-plane equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Hao Zhu, Luqi Wang, Zhifei Zhang","submitted_at":"2022-02-11T15:43:04Z","abstract_excerpt":"In this paper, we study stationary structures near the planar Couette flow in Sobolev spaces on a channel $\\mathbb{T}\\times[-1,1]$, and asymptotic behavior of Couette flow in Gevrey spaces on $\\mathbb{T}\\times\\mathbb{R}$ for the $\\beta$-plane equation. Let $T>0$ be the horizontal period of the channel and $\\alpha={2\\pi\\over T}$ be the wave number. We obtain a sharp region $O$ in the whole $(\\alpha,\\beta)$ half-plane such that non-parallel steadily traveling waves do not exist for $(\\alpha,\\beta)\\in O$ and such traveling waves exist for $(\\alpha,\\beta)$ in the remaining regions, near Couette fl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.05708","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.05708/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}